If standard quantum theory holds up, imaginary numbers are critical. When you purchase through links on our site, we may earn an affiliate commission. Here’s how it works. Imaginary numbers are ...

Real and imaginary: The time-dependent Schrödinger equation formulated using complex numbers. (Courtesy: iStock/piranka) Complex numbers are essential to achieve the most accurate quantum-mechanical ...

In 2020 one of us, Toni, asked another of us, Marco, to come to his office at the Institute of Photonic Sciences, a large research center in Castelldefels near Barcelona. “There is a problem that I ...

The purpose of this paper is to give formulas and Recurrence relations for the Apostol-Euler numbers and polynomials of order with complex numbers with the aid of the Euler operator and partial ...